In the case of one-dimensional steady-state heat flow through a sample body, its thermal conductivity K is given by EQU K=P/A(.DELTA.T/.DELTA.x) (1)
where P is the heat flowing per unit time along the x axis through a cross section of the body, the cross section being oriented parallel to the yz plane and having an area equal to A, and where .DELTA.T is the temperature drop along a distance .DELTA.x measured along the x axis as can be measured by attaching to the body a pair of localized temperature sensors (thermometers), typically thermocouple junctions (thermocouples), that are spaced apart in the x direction by the distance .DELTA.x. A direct measurement technique that implements this one-dimensional heat flow is generally described in the textbook Elementary Physics: Classical and Modern, by Richard T. Weidner and Robert L. Sells, at pages 306-307 (1975).
In that technique, a sample body in the form of a solid circular cylinder ("rod"), having a uniform cross section A and having a pair of end surfaces, is surrounded by an insulating material, in order to minimize heat exchange into or out of the sample body through its side surfaces. One end surface of the body is maintained at a constant high temperature T.sub.h, as by means of a hot reservoir or heat source, while the other end surface is maintained at a constant lower temperature T.sub.c, as by means of a cold reservoir or heat sink. In the steady state, the heat crossing any cross section of the cylinder per unit time is equal to the same value P given by eq. (1) above, and the temperature gradient .DELTA.T/.DELTA.x is the same everywhere along the rod, i.e., is independent of the x coordinate.
In prior art, implementation of this sort of one-dimensional technique has been cumbersome and time-consuming, stemming from the need for attaching the heat reservoirs and the thermometers to the sample body each time a different one is to be measured. Also, relatively lengthy and careful measurements are required to account for, and correct for, heat losses. More specifically, the required thermal insulation tends to get in the way of the thermometers (thermocouple junctions) and their wiring, as well as in the way of the heat source and its wiring--the wiring, being fine (small diameter) and fragile, and having a tendency to develop kinks and to be crunched by the required thermal insulating material.
Turning to the case of a circularly symmetric radial heat flow P, in the steady state the thermal conductivity K of a sample body is given by ##EQU1## where T1 and T2 are the temperatures at radial distances R1 and R2 from a point on the body located at the center of circular symmetry, and where h is the thickness of the body measured parallel to its z axis, i.e., measured perpendicular to the xy plane in which the radial heat flow P is occurring. For example, the sample body was in the form of a circular cylinder having a pair of end surfaces spaced apart by h. In prior art, because of the problem of radiation and other heat losses, it was necessary that h be made much greater (by a factor of at least approximately ten) than R2 in order to ensure that the heat flow was radial. In this way, the heat flow was radial, so that K could be determined from eq. (2). However, in order to minimize errors caused by end effects, it was necessary to measure the temperatures T1 and T2 at interior points of the sample body--i.e., at points located in the midst of the sample (away from its end surfaces)--which rendered the measuring process cumbersome and time-consuming.
Moreover, the geometry of a relatively thin plate does not satisfy the aforementioned limitation on its thickness h, and therefore accurate measurements of the thermal conductivity of such a plate cannot be achieved by means of the above-described prior-art radial-heat-flow technique.
Therefore, it would be desirable to have method and apparatus for measuring the thermal conductivity of a sample body in a relatively quick and easy manner.